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%I #48 Jul 10 2022 09:43:05
%S 0,1,2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,
%T 2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,2,3,4,5,6,7,0,1,2,3,
%U 4,5,6,7,0,1,2,3,4,5,6,7,0
%N a(n) = n mod 8.
%C The rightmost digit in the base-8 representation of n. Also, the equivalent value of the three rightmost digits in the base-2 representation of n. - _Hieronymus Fischer_, Jun 12 2007
%H Antti Karttunen, <a href="/A010877/b010877.txt">Table of n, a(n) for n = 0..65536</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).
%F Complex representation: a(n) = (1/8)*(1-r^n)*Sum_{k=1..7} k*Product_{m=1..7, m<>k} (1 - r^(n-m)) where r = exp(Pi/4*i) = (1+i)*sqrt(2)/2 and i=sqrt(-1).
%F Trigonometric representation: a(n) = 256*(sin(n*Pi/8))^2*Sum_{k=1..7} k*Product_{m=1..7, m<>k} (sin((n-m)*Pi/8))^2.
%F G.f.: g(x) = (Sum_{k=1..7}, k*x^k)/(1-x^8).
%F Also: g(x) = x(7x^8-8x^7+1)/((1-x^8)(1-x)^2). - _Hieronymus Fischer_, May 31 2007
%F a(n) = n mod 2 + 2*(floor(n/2) mod 4) = A000035(n) + 2*A010873(A004526(n)).
%F a(n) = n mod 4 + 4*(floor(n/4) mod 2) = A010873(n) + 4*A000035(A002265(n)).
%F a(n) = n mod 2 + 2*(floor(n/2) mod 2) + 4*(floor(n/4) mod 2) = A000035(n) + 2*A000035(A004526(n))) + 4*A000035(A002265(n)). - _Hieronymus Fischer_, Jun 12 2007
%F a(n) = (1/2)*(7 - (-1)^n - 2*(-1)^(b/4) - 4*(-1)^((b - 2 + 2*(-1)^(b/4))/8)) where b = 2n - 1 + (-1)^n. - _Hieronymus Fischer_, Jun 12 2007
%F General formula for period 2^k: a(n) = (1/2)*(2^k - 1 - Sum_{j=0..k-1} 2^j*(-1)^p(j,n)) where p(j,n) is defined recursively by p(0,n)=n, p(j,n) = (1/4)*(2*p(j-1,n) - 1 + (-1)^p(j-1,n)). - _Hieronymus Fischer_, Jun 14 2007
%F a(n) = floor(1234567/99999999*10^(n+1)) mod 10. - _Hieronymus Fischer_, Jan 03 2013
%F a(n) = floor(48913/2396745*8^(n+1)) mod 8. - _Hieronymus Fischer_, Jan 04 2013
%t Table[Mod[n,8],{n,0,120}] (* _Harvey P. Dale_, Apr 21 2011 *)
%o (PARI) vector(100,i,i)%8 \\ _Charles R Greathouse IV_, Jul 16 2011
%o (Python)
%o def A010877(n): return n&7 # _Chai Wah Wu_, Jul 09 2022
%Y Partial sums: A130486. Other related sequences A130481, A130482, A130483, A130484, A130485.
%Y Cf. A000035, A010887, A010873, A130909, A168181, A244413, A253513.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Formula section re-edited for better readability by _Hieronymus Fischer_
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